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Holographic storage stability in PQ-PMMA bulk photopolymer
Optics Communications 283 (2010) 4219–4223
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Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Holographic storage stability in PQ-PMMA bulk photopolymer Dan Yu, Hongpeng Liu, Yongyuan Jiang, Xiudong Sun ⁎ Department of Physics, Harbin Institute of Technology, Harbin, 150001, PR China
a r t i c l e
i n f o
Article history: Received 1 February 2010 Received in revised form 7 June 2010 Accepted 7 June 2010 Keywords: Storage stability Photopolymer Holographic volume grating
a b s t r a c t Holographic storage stability is investigated experimentally in phenanthrenequinone (PQ) doped poly(methyl methacrylate) (PMMA) photopolymer with high thickness and rigid polymer matrix. It is demonstrated that the stability consists of two continuous processes, dark enhancement and decay of holograms, which are corresponding to the diffusion of PQ and its photoproduct molecules, respectively. During dark enhancement the Bragg detuning of angle selectivity is observed. Therefore it is necessary to obtain steady holograms quality by adjusting the readout angle. After reaching steady state, the long-term stability of holograms is determined by the diffusion of photoproducts. Temperature is a most significant parameter for long-term stability, which can bring sufficient energy to increase the diffusion of photoproducts and reduce the stability. Finally low temperature and uniform exposure as alternative methods are proposed to optimize the storage stability after dark enhancement. Moreover the influence of humidity on the storage stability is neglectable. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Photopolymers are attractive materials for holographic data storage, information process and other display applications [1–3]. In the development of high quality materials many aspects must be considered, such as high diffraction efficiency, high thickness (≥500 μm), and temporal stability of holograms [4–7]. The storage stability is one of the most significant parameters for applicability of holographic recording materials [7,8]. So far, the stabilities in some photopolymers have been investigated in the experiments [9,10]. Thousands of weak holograms with optical information are recorded onto one location of a material for high density storage. Due to low modulated depth of holograms the lifetimes of recorded information are effected consequently by many factors, such as component diffusions and environmental conditions. One of the significant influences on the stability in fact is the diffusion of primary components from dark region into bright region. Dark enhancement and decay are main features of holograms stability in material with high thickness and rigid polymer matrix like phenanthrenequinone (PQ) doped poly(methyl methacrylate) (PMMA) photopolymer [11– 14]. The PQ-PMMA photopolymers are known as effective holographic recording materials due to their excellent ability to form thick mediums that exhibit high diffractive efficiency [11–18]. The application of the materials for high density storage and optical elements has attracted much attention [19–23]. However the investigation of environmental condition for improving holographic
⁎ Corresponding author. Tel./fax: + 86 451 86414129. E-mail address: [email protected] (X. Sun). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.06.026
storage stability has not attracted much attention. So far, the storage stability of weak holograms in the photopolymer has seldom been studied. In this paper the measurement and improvement of holograms stability are investigated. We observe the influence of internal and external factors on temporal stability of holograms, and provide appropriated methods for optimizing the stability.
2. Materials and experiments In our experiments, the PQ-PMMA sample was used to holographic recording. The thermal initiator 2, 2-azobis (2-methlpropionitrile) (AIBN) and PQ molecules were dissolved in a solvent methyl methacrylate (MMA) and mixed to form a uniform solution. The mixture was poured into a glass mold and solidified at 60 °C for 120 h. After the thermal polymerization, the sample with PQ's concentration 0.1 M and thickness 2 mm was prepared. Two beams coupling setup with 90° geometry was used to record an unslanted transmission grating, as shown in Fig. 1. The recording beams were directed to the intersect inside sample with respect to the sample normal. The input images were represented on spatial light modulator (SLM). The recording intensities of reference and signal beams with 532 nm were 509 mW/cm2 and 152 mW/cm2, respectively, and the recording exposure time was 4 s. The sample was placed on a computer-controlled motorized stage with 0.0025° to allow Bragg angle tuning of probe beam. The rotating axis of rotation stage is perpendicular to the recording beams plane. For reconstruction the reference beam attenuated to tenth of the initial value was used, and the holograms were detected by CCD.
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½PhotoproductsðxÞ = ½PQ 0 −½PQ ðte Þ½1 + V cosð2πx = ΛÞ:
ð6Þ
The distribution profiles of PQ molecules and its photoproducts are approximately proportional to [1 + Vcos(2πx/Λ)] and [1 − Vcos(2πx/ Λ)], respectively. Therefore after exposure time te, the change of refractive index which is related to the components concentration can be described as [26] δn∝CPQ Δ½PQ ½1 + V cosð2πx = ΛÞ
ð7Þ
+ CP Δ½Photoproduct ½1−V cosð2πx = ΛÞ
Fig. 1. Schematic diagram of a 90°-geometry experimental setup: A1 A2, apertures, PBS, polarizing beam-splitter, SF, spatial filter, SLM, spatial light modulator, S, shutter, M1, M2, mirrors, L, lens.
3. Results and discussion The stability of data storage can be described as archival life of holograms in darkness. This process consists of two consecutive processes, dark enhancement and dark decay of holograms, which are the temporal evolution of hologram quality [11–13]. Firstly we analyze the dark enhancement of holograms under short exposure. The dark decay as a disadvantage of long-term stability is then investigated. During this process the environmental stability, in particular thermal stability, is discussed experimentally. Finally an optimal strategy was used to improve the stability.
3.1. Photochemical mechanism To discuss the stability of data storage in the materials, we must briefly analyze the photochemical mechanism involved. Under illumination the PQ molecules are photoexcited. The complex photochemical processes can be simply described as [14,18,19], 3
PQ→ PQ 3
ð1Þ •
•
PQ þ HR→HPQ þ R ; •
•
Rn−1 þ R→Rn ; •
•
HPQ þ Rn →HPQ−nR;
ð2Þ
ð3Þ
ð4Þ
where CPQ and CP are constants related to the component refractive index. The corresponding change of refractive index can be given by δn x; t ′
′ = CPQ A exp −t = τ 1 ½1 + V cosð2πx = ΛÞ + CP B exp −t ′ = τ 2 ½1−V cosð2πx = ΛÞ h i ′ ′ ′ ′ = A exp −t = τ 1 −B exp −t = τ2 V cosð2πx = ΛÞ + A′ exp −t ′ = τ1 + B′ exp −t ′ = τ 2
ð8Þ
where t ′ = t − te represents the beginning from the moment when the recording beams are turned off. τ1 and τ2 are the diffusion time constants of PQ molecules and its photoproducts. A, B is modulation amplitude which related to the component concentrations. The last term is un-modulated refractive index decaying background and does not contribute to the index modulation. The diffusion time constant τ = Λ2/4π2D, D is diffusion coefficient. Thus the temporal evolution of refractive index modulation can approximately be given by ′ ′ 2 ′ 2 ′ 2 ′ 2 Δn t = A exp −4π DPQ t = Λ −B exp −4π DP t = Λ ;
ð9Þ
where DPQ and DP are the diffusion coefficients of PQ molecules and its photoproducts. 3.2. Dark enhancement of holograms In order to describe the temporal stability of holograms, we measured the dark enhancement process of holograms and observed the amplification of Bragg detuning of angle selectivity. The typical enhancement curve of hologram is shown in Fig. 2. The dark development trend is similar as exponential function, and it is implied that the PQ's diffusion is a key parameter to determine the dark enhancement. However the amplification of Bragg detuning is observed in this process, as shown in Fig. 3. Due to the amplification of holographic
where R represents the MMA molecules (n ≥ 1). There are two offsetting gratings in the exposure spot. One of these gratings consists of photoexcited PQ molecules and the other consists of free PQ molecules [13]. Diffusions of the free PQ molecules and photoproducts play an important role in the temporal evolution of stability, which lead to the dark enhancement and decay of diffraction efficiency, respectively [12]. The chemical spectra measurement [24,25] indicated that the primary photoproducts are PQ-nMMA oligomers in incompletely photopolymer like our sample, and its diffusions are primary factors effected on the dark decay dynamics. It is well-known that the distribution of intensity in the intersecting spot is given by I = I0[1 + Vcos(2πx/Λ)], where Λ is the fringe space. As consequence after exposure time te the free PQ molecules and photoproducts can be depicted as [14] ½PQ ðxÞ = ½PQ ðte Þ½1 + V cosð2πx = ΛÞ;
ð5Þ
Fig. 2. Dark enhancement of holograms, t = 0 presents the exposure turn-off. The solid lines are fitting curves using exponential function.
D. Yu et al. / Optics Communications 283 (2010) 4219–4223
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Fig. 3. (a) Temporal stability of holograms, t = 0 presents the exposure turn-off. The hollow and solid symbols correspond to the reconstructions at original recording position and adjusted position by rotating sample, respectively. (b) Corresponding dark enhancement processes of holograms in 6000 s time scale in (a), the solid line is exponential fitting. (c) Corresponding temporal evolution of holograms quality.
gratings induced by diffusion of PQ's molecules, the diffraction efficiency of hologram is obviously increased after recording exposure. However the weak increments of holograms are observed at original recording position in Fig. 3(a) by hollow squares. By rotating the sample to adjust the reading angles, we readout the hologram every time at peak value of Bragg angle selectivity, and steady increment values are obtained in Fig. 3(a) by solid squares. Fig. 3(b) shows the dark enhancement process of holograms using normal time scale in Fig. 3(a), and the solid lines are exponential fitting. The corresponding experimental results are shown in Fig. 3(c). It should be noted that the low increment of hologram can be attributed to the amplification of Bragg detuning [27]. In this process the non-uniform hologram is observed, and the distorting of holograms is not observed. It can be attributed to the rigid polymer matrix that resulted in the integral shift of grating fringes during shrinkage. The dark reaction and PQ's diffusion, which enhanced the modulated depth of weak gratings, are the primary factors that bring about the shrinkage of holograms. After short exposure the initial shift of Bragg selectivity curve comes from the dark reaction, because the intermolecular distances are substituted by the carbon–carbon bonds. However the dark reaction process is quite transitory due to short lifetime of radicals, and the consecutive diffusion of PQ molecules subsequently amplified the shrinkage of holographic gratings and finally brought the low increment of modulation. At the same time the decayed reference beam as reading beam can also increased the dark polymerization of radicals despite the short reading times, which can also bring to the slight shrinkage during dark enhancement and dark decay. Therefore it is necessary to improve the storage stability by adjusting the readout angle. In the following experiments, we monitored the holograms by using corresponding peak values of Bragg selectivity curve.
environmental temperature is one of most significant parameters for influencing the diffusion of photoproducts. In this section the effect of temperature on the long-term stability of holograms is investigated experimentally. A hologram firstly is written with 4 s exposure time, and the dark enhancement process of holograms is observed at normal temperature. After reaching steady state of the dark enhancement, the sample then was taken into an oven for thermal treatment, and the temporal evolution of hologram qualities was measured by the peak values of Bragg selectivity curve. The same set of experiments is repeated for several temperatures, namely − 10, 35, 40, 50, and 60 °C. Fig. 4 shows the temperature stability of holograms after dark enhancement. The dash line presents the initial time for thermal treatment. It can be seen that the curve firstly rises and reaches a steady state at room temperature, then gradually decreases by
3.3. Dark decay of holograms After reaching steady state of dark enhancement, the stability of holograms is determined by diffusion of photoproducts. Here the
Fig. 4. Temperature stability of holograms, t = 0 presents the exposure turn-off. The symbols are corresponding to different temperatures. Black dash is the initial time for thermal treatment.
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Fig. 5. Temperature stability of holograms SNR, t = 0 presents the exposure turn-off. The symbols are corresponding to different temperatures. Black dash is the initial time for thermal treatment.
thermal treatment. At low temperature for example −10 °C, the hologram efficiency keeps up a constant and only slightly decreases for a long time. The higher the temperature, the higher the decay rate of holograms is. The slight differences in enhancement rates come from the fluctuation of incident intensity and in-homogeneity of sample. Then the SNR of images were calculated to describe the hologram qualities [2] m2 −m1 SNR = qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; σ12 + σ22
ð10Þ
where m1 and σ1 are the mean and standard deviations for the dark pixels. Similarly, m2 and σ2 are the mean and standard deviations for the white pixels, respectively. The temperature stability of holograms SNR is shown in Fig. 5. As can be seen that the SNR of holograms increased monotonically during dark enhancement, and then it also keeps up a steady value at the low temperature. This process can be attributed to the increment of strong grating in white pixels is obviously higher than that of weak grating in dark pixels, despite rate of the later is higher. In order to demonstrate the decay of hologram quality is related to the diffusion of photoproducts, the time constant τ of decay curve is extracted by nonlinear fitting using Eq. (9). The corresponding diffusion coefficient can be calculated. The temperature dependence of diffusion coefficient is illuminated in Fig. 6. The relationship between diffusion coefficient and temperature for T b Tg can be depicted as [26],
Fig. 7. Lifetime of weak gratings as a function of environmental temperature.
where C1, C2 are the Williams–Landel–Ferry (WLF) coefficients which can be used to described the diffusion process dependent on the temperature. The good agreement between experimental data and theoretical values demonstrates that the decay of stability depended on the diffusion of photoproducts. The characteristic time of decay curves is defined as lifetime of gratings for describing the stability. Fig. 7 represents the lifetime of weak hologram as a function of temperature. The lifetime is remarkably increased as the temperature is reduced. It is indicated that an appropriated temperature can be brought near year lifetime. This curve simultaneously implies that the lifetime of weak hologram is shorter than the lifetime of strong grating which is similar as reference [28].
3.4. Uniform incoherent exposure
ð11Þ
So far, several methods have been presented to improve the stability, such as uniform coherent and incoherent illumination [9,10], baking the sample after exposure [15], and changing the polymerization mechanism [29]. The coherent illumination may bring an amplification of holographic scattering noise and reduction of hologram quality. Therefore final uniform incoherent illumination is an alternative and a simple method for keeping up the long-term stability of holograms, which can be consumed by all the remaining free PQ molecules in the photopolymer. Therefore further holographic recording is prevented. At the saturation of dark enhancement the unreacted PQ molecules are exhausted by uniform exposure, and the exposure time is around 5 h for using up all the free PQ molecules. Then the sample is taken into an oven at 35 °C for thermal treatment. The temporal stability of hologram is measured, as shown in Fig. 8.
Fig. 6. Diffusion coefficient of photoproduct versus temperature. The symbols are the experimental data, and the solid line is fitting curve. The experimental accuracy approached 5%.
Fig. 8. The influence of uniform incoherent exposure on the stability of holograms. The solid and hollow symbols are corresponding to uniform exposure and un-exposure, respectively. The dashes are the corresponding initial time for thermal treatment.
ln ½DðT Þ = C1 = T + C2
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The stability of weak holograms is an important factor for holographic memory. The combination of low temperature and uniform incoherent exposure is the appropriated method for improving the storage stability. This study can improve the understanding of photochemical behaviors and accelerate applicability of PQ-PMMA photopolymers in holographic data storage. Acknowledgements The research has been financially supported by the Fundamental Research Foundation of Commission of Science Technology and Industry for National Defense of China (Grant No. 2320060089).
Fig. 9. The influence of relative humidity on the stability of holograms.
The maximum of refractive index modulation is observed at exposure process. It is implied that the uniform exposure is an efficient method to improving the stability of holograms. Thermal treatment slightly decreases the modulated depth because the photopolymer chains by uniform exposure cannot completely restrain the diffusion of macromolecules of holographic gratings. 3.5. The effect of humidity on hologram qualities Finally the influence of the relative humidity on qualities of holograms is experimentally investigated. We firstly written a hologram in the sample at room temperature, then changed the relative humidity of condition after steady state. The diffraction efficiency and SNR of hologram as a function of relative humidity are shown in Fig. 9. The high humidity can increase the scattered light by vapor and reduce the transmittance of sample, since the qualities of reading holograms would be decreased. However the influence of slight reduction of these values on the stability of holograms is neglectable due to the rigid polymer matrix. 4. Conclusion A detailed experimental study of storage stability in PQ-PMMA photopolymers is presented. The amplification of Bragg detuning was observed during dark diffusion, therefore we must adjust the reading angle for reconstruction. It is demonstrated that the temperature stability of holograms was related to the diffusion of photoproducts.
References [1] H.S. Li, D. Psaltis, Appl. Opt. 33 (1994) 3764. [2] A. Pu, D. Psaltis, Appl. Opt. 35 (1996) 2389. [3] H.J. Coufal, D. Psaltis, G.T. Sincerbox (Eds.), Holographic Data Storage, SpringerVerlag, New York, 2000. [4] L. Dhar, K. Curtis, M. Tackitt, M.L. Schilling, S. Campbell, Opt. Lett. 23 (1998) 1710. [5] P. Cheben, M.L. Calvo, Appl. Phys. Lett. 78 (2001) 1490. [6] E. Fernandez, C. Garcia, I. Pascual, M. Ortuno, S. Gallego, A. Belendez, Appl. Opt. 45 (2006) 7661. [7] S. Blaya, L. Carretero, R. Mailavia, A. Fimia, R.F. Madrigal, M. Ulibarrena, D. Levy, Appl. Opt. 37 (1998) 7604. [8] K. Tsuchida, M. Ohkawa, S. Sekine, Proc. of SPIE 6136 (2006) 613610. [9] S. Gallego, C. Neipp, M. Ortuño, A. Beléndez, I. Pascual, J. Mod. Opt. 51 (2004) 491. [10] T.C. Felder, S.H. Stevenson, P.J. O'Connor, R.M. Yohannan, Proc. SPIE 3956 (2000) 314. [11] A.V. Veniaminov, Yu.N. Sedunov, Polymer Science Ser. A. 38 (1996) 56. [12] A.V. Veniaminov, H. Sillescu, Chem. Phys. Lett. 303 (1999) 499. [13] A.V. Veniaminov, E. Bartsch, J. Opt. A Pure Appl. Opt. 4 (2002) 387. [14] H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, X. Sun Opt. Express 18 (2010) 6447. [15] G.J. Steckman, I. Solomatine, G. Zhou, D. Psaltis, Opt. Lett. 23 (1998) 1310. [16] S.H. Lin, K.Y. Hsu, W.Z. Chen, W.T. Whang, Opt. Lett. 25 (2000) 451. [17] S.H. Lin, K.Y. Hsu, Proc. SPIE 4110 (2000) 77. [18] H. Liu, D. Yu, Y. Jiang, X. Sun, Appl. Phys. B 95 (2009) 513. [19] V. Matusevich, A. Matusevich, R. Kowarschik, Yu.I. Matusevich, L.P. Krul, Opt. Express 16 (2008) 1552. [20] A. Popov, I. Novikov, K. Lapushka, I. Zyuzin, Y. Ponosov, Y. Ashcheulov, A.V. Veniaminov, J. Opt. A Pure and Appl. Opt. 2 (2000) 494. [21] A. Sato, R.K. Kostuk, Proc. SPIE 5216 (2003) 44. [22] Y. Luo, P.J. Gelsinger, J.K. Barton, G. Barbastathis, R.K. Kostuk, Opt. Lett. 33 (2008) 566. [23] Y. Luo, P.J. Gelsinger-Austin, J.M. Watson, G. Barbastathis, J.K. Barton, R.K. Kostuk, Opt. Lett. 33 (2008) 2098. [24] Yi-Nan Hsiao, W.T. Whang, S.H. Lin, Opt. Eng. 43 (9) (2004) 1993. [25] A.V. Veniaminov, H. Sillescu, Macromolecules 32 (1999) 1828. [26] J. Zhang, C.H. Wang, Macromolecules 20 (1987) 2296. [27] J. Wang, X. Sun, S. Luo, Y. Jiang, Opt. Mater. 32 (2009) 261. [28] I. Semenova, A. Popov, E. Bartsch, A. Veniaminov, Proc. SPIE 5005 (2003) 1. [29] D.A. Waldman, C.J. Butler, D.H. Raguin, Proc. SPIE 5216 (2003) 10.
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Holographic storage stability in PQ-PMMA bulk photopolymer Dan Yu, Hongpeng Liu, Yongyuan Jiang, Xiudong Sun ⁎ Department of Physics, Harbin Institute of Technology, Harbin, 150001, PR China
a r t i c l e
i n f o
Article history: Received 1 February 2010 Received in revised form 7 June 2010 Accepted 7 June 2010 Keywords: Storage stability Photopolymer Holographic volume grating
a b s t r a c t Holographic storage stability is investigated experimentally in phenanthrenequinone (PQ) doped poly(methyl methacrylate) (PMMA) photopolymer with high thickness and rigid polymer matrix. It is demonstrated that the stability consists of two continuous processes, dark enhancement and decay of holograms, which are corresponding to the diffusion of PQ and its photoproduct molecules, respectively. During dark enhancement the Bragg detuning of angle selectivity is observed. Therefore it is necessary to obtain steady holograms quality by adjusting the readout angle. After reaching steady state, the long-term stability of holograms is determined by the diffusion of photoproducts. Temperature is a most significant parameter for long-term stability, which can bring sufficient energy to increase the diffusion of photoproducts and reduce the stability. Finally low temperature and uniform exposure as alternative methods are proposed to optimize the storage stability after dark enhancement. Moreover the influence of humidity on the storage stability is neglectable. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Photopolymers are attractive materials for holographic data storage, information process and other display applications [1–3]. In the development of high quality materials many aspects must be considered, such as high diffraction efficiency, high thickness (≥500 μm), and temporal stability of holograms [4–7]. The storage stability is one of the most significant parameters for applicability of holographic recording materials [7,8]. So far, the stabilities in some photopolymers have been investigated in the experiments [9,10]. Thousands of weak holograms with optical information are recorded onto one location of a material for high density storage. Due to low modulated depth of holograms the lifetimes of recorded information are effected consequently by many factors, such as component diffusions and environmental conditions. One of the significant influences on the stability in fact is the diffusion of primary components from dark region into bright region. Dark enhancement and decay are main features of holograms stability in material with high thickness and rigid polymer matrix like phenanthrenequinone (PQ) doped poly(methyl methacrylate) (PMMA) photopolymer [11– 14]. The PQ-PMMA photopolymers are known as effective holographic recording materials due to their excellent ability to form thick mediums that exhibit high diffractive efficiency [11–18]. The application of the materials for high density storage and optical elements has attracted much attention [19–23]. However the investigation of environmental condition for improving holographic
⁎ Corresponding author. Tel./fax: + 86 451 86414129. E-mail address: [email protected] (X. Sun). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.06.026
storage stability has not attracted much attention. So far, the storage stability of weak holograms in the photopolymer has seldom been studied. In this paper the measurement and improvement of holograms stability are investigated. We observe the influence of internal and external factors on temporal stability of holograms, and provide appropriated methods for optimizing the stability.
2. Materials and experiments In our experiments, the PQ-PMMA sample was used to holographic recording. The thermal initiator 2, 2-azobis (2-methlpropionitrile) (AIBN) and PQ molecules were dissolved in a solvent methyl methacrylate (MMA) and mixed to form a uniform solution. The mixture was poured into a glass mold and solidified at 60 °C for 120 h. After the thermal polymerization, the sample with PQ's concentration 0.1 M and thickness 2 mm was prepared. Two beams coupling setup with 90° geometry was used to record an unslanted transmission grating, as shown in Fig. 1. The recording beams were directed to the intersect inside sample with respect to the sample normal. The input images were represented on spatial light modulator (SLM). The recording intensities of reference and signal beams with 532 nm were 509 mW/cm2 and 152 mW/cm2, respectively, and the recording exposure time was 4 s. The sample was placed on a computer-controlled motorized stage with 0.0025° to allow Bragg angle tuning of probe beam. The rotating axis of rotation stage is perpendicular to the recording beams plane. For reconstruction the reference beam attenuated to tenth of the initial value was used, and the holograms were detected by CCD.
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D. Yu et al. / Optics Communications 283 (2010) 4219–4223
½PhotoproductsðxÞ = ½PQ 0 −½PQ ðte Þ½1 + V cosð2πx = ΛÞ:
ð6Þ
The distribution profiles of PQ molecules and its photoproducts are approximately proportional to [1 + Vcos(2πx/Λ)] and [1 − Vcos(2πx/ Λ)], respectively. Therefore after exposure time te, the change of refractive index which is related to the components concentration can be described as [26] δn∝CPQ Δ½PQ ½1 + V cosð2πx = ΛÞ
ð7Þ
+ CP Δ½Photoproduct ½1−V cosð2πx = ΛÞ
Fig. 1. Schematic diagram of a 90°-geometry experimental setup: A1 A2, apertures, PBS, polarizing beam-splitter, SF, spatial filter, SLM, spatial light modulator, S, shutter, M1, M2, mirrors, L, lens.
3. Results and discussion The stability of data storage can be described as archival life of holograms in darkness. This process consists of two consecutive processes, dark enhancement and dark decay of holograms, which are the temporal evolution of hologram quality [11–13]. Firstly we analyze the dark enhancement of holograms under short exposure. The dark decay as a disadvantage of long-term stability is then investigated. During this process the environmental stability, in particular thermal stability, is discussed experimentally. Finally an optimal strategy was used to improve the stability.
3.1. Photochemical mechanism To discuss the stability of data storage in the materials, we must briefly analyze the photochemical mechanism involved. Under illumination the PQ molecules are photoexcited. The complex photochemical processes can be simply described as [14,18,19], 3
PQ→ PQ 3
ð1Þ •
•
PQ þ HR→HPQ þ R ; •
•
Rn−1 þ R→Rn ; •
•
HPQ þ Rn →HPQ−nR;
ð2Þ
ð3Þ
ð4Þ
where CPQ and CP are constants related to the component refractive index. The corresponding change of refractive index can be given by δn x; t ′
′ = CPQ A exp −t = τ 1 ½1 + V cosð2πx = ΛÞ + CP B exp −t ′ = τ 2 ½1−V cosð2πx = ΛÞ h i ′ ′ ′ ′ = A exp −t = τ 1 −B exp −t = τ2 V cosð2πx = ΛÞ + A′ exp −t ′ = τ1 + B′ exp −t ′ = τ 2
ð8Þ
where t ′ = t − te represents the beginning from the moment when the recording beams are turned off. τ1 and τ2 are the diffusion time constants of PQ molecules and its photoproducts. A, B is modulation amplitude which related to the component concentrations. The last term is un-modulated refractive index decaying background and does not contribute to the index modulation. The diffusion time constant τ = Λ2/4π2D, D is diffusion coefficient. Thus the temporal evolution of refractive index modulation can approximately be given by ′ ′ 2 ′ 2 ′ 2 ′ 2 Δn t = A exp −4π DPQ t = Λ −B exp −4π DP t = Λ ;
ð9Þ
where DPQ and DP are the diffusion coefficients of PQ molecules and its photoproducts. 3.2. Dark enhancement of holograms In order to describe the temporal stability of holograms, we measured the dark enhancement process of holograms and observed the amplification of Bragg detuning of angle selectivity. The typical enhancement curve of hologram is shown in Fig. 2. The dark development trend is similar as exponential function, and it is implied that the PQ's diffusion is a key parameter to determine the dark enhancement. However the amplification of Bragg detuning is observed in this process, as shown in Fig. 3. Due to the amplification of holographic
where R represents the MMA molecules (n ≥ 1). There are two offsetting gratings in the exposure spot. One of these gratings consists of photoexcited PQ molecules and the other consists of free PQ molecules [13]. Diffusions of the free PQ molecules and photoproducts play an important role in the temporal evolution of stability, which lead to the dark enhancement and decay of diffraction efficiency, respectively [12]. The chemical spectra measurement [24,25] indicated that the primary photoproducts are PQ-nMMA oligomers in incompletely photopolymer like our sample, and its diffusions are primary factors effected on the dark decay dynamics. It is well-known that the distribution of intensity in the intersecting spot is given by I = I0[1 + Vcos(2πx/Λ)], where Λ is the fringe space. As consequence after exposure time te the free PQ molecules and photoproducts can be depicted as [14] ½PQ ðxÞ = ½PQ ðte Þ½1 + V cosð2πx = ΛÞ;
ð5Þ
Fig. 2. Dark enhancement of holograms, t = 0 presents the exposure turn-off. The solid lines are fitting curves using exponential function.
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Fig. 3. (a) Temporal stability of holograms, t = 0 presents the exposure turn-off. The hollow and solid symbols correspond to the reconstructions at original recording position and adjusted position by rotating sample, respectively. (b) Corresponding dark enhancement processes of holograms in 6000 s time scale in (a), the solid line is exponential fitting. (c) Corresponding temporal evolution of holograms quality.
gratings induced by diffusion of PQ's molecules, the diffraction efficiency of hologram is obviously increased after recording exposure. However the weak increments of holograms are observed at original recording position in Fig. 3(a) by hollow squares. By rotating the sample to adjust the reading angles, we readout the hologram every time at peak value of Bragg angle selectivity, and steady increment values are obtained in Fig. 3(a) by solid squares. Fig. 3(b) shows the dark enhancement process of holograms using normal time scale in Fig. 3(a), and the solid lines are exponential fitting. The corresponding experimental results are shown in Fig. 3(c). It should be noted that the low increment of hologram can be attributed to the amplification of Bragg detuning [27]. In this process the non-uniform hologram is observed, and the distorting of holograms is not observed. It can be attributed to the rigid polymer matrix that resulted in the integral shift of grating fringes during shrinkage. The dark reaction and PQ's diffusion, which enhanced the modulated depth of weak gratings, are the primary factors that bring about the shrinkage of holograms. After short exposure the initial shift of Bragg selectivity curve comes from the dark reaction, because the intermolecular distances are substituted by the carbon–carbon bonds. However the dark reaction process is quite transitory due to short lifetime of radicals, and the consecutive diffusion of PQ molecules subsequently amplified the shrinkage of holographic gratings and finally brought the low increment of modulation. At the same time the decayed reference beam as reading beam can also increased the dark polymerization of radicals despite the short reading times, which can also bring to the slight shrinkage during dark enhancement and dark decay. Therefore it is necessary to improve the storage stability by adjusting the readout angle. In the following experiments, we monitored the holograms by using corresponding peak values of Bragg selectivity curve.
environmental temperature is one of most significant parameters for influencing the diffusion of photoproducts. In this section the effect of temperature on the long-term stability of holograms is investigated experimentally. A hologram firstly is written with 4 s exposure time, and the dark enhancement process of holograms is observed at normal temperature. After reaching steady state of the dark enhancement, the sample then was taken into an oven for thermal treatment, and the temporal evolution of hologram qualities was measured by the peak values of Bragg selectivity curve. The same set of experiments is repeated for several temperatures, namely − 10, 35, 40, 50, and 60 °C. Fig. 4 shows the temperature stability of holograms after dark enhancement. The dash line presents the initial time for thermal treatment. It can be seen that the curve firstly rises and reaches a steady state at room temperature, then gradually decreases by
3.3. Dark decay of holograms After reaching steady state of dark enhancement, the stability of holograms is determined by diffusion of photoproducts. Here the
Fig. 4. Temperature stability of holograms, t = 0 presents the exposure turn-off. The symbols are corresponding to different temperatures. Black dash is the initial time for thermal treatment.
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Fig. 5. Temperature stability of holograms SNR, t = 0 presents the exposure turn-off. The symbols are corresponding to different temperatures. Black dash is the initial time for thermal treatment.
thermal treatment. At low temperature for example −10 °C, the hologram efficiency keeps up a constant and only slightly decreases for a long time. The higher the temperature, the higher the decay rate of holograms is. The slight differences in enhancement rates come from the fluctuation of incident intensity and in-homogeneity of sample. Then the SNR of images were calculated to describe the hologram qualities [2] m2 −m1 SNR = qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; σ12 + σ22
ð10Þ
where m1 and σ1 are the mean and standard deviations for the dark pixels. Similarly, m2 and σ2 are the mean and standard deviations for the white pixels, respectively. The temperature stability of holograms SNR is shown in Fig. 5. As can be seen that the SNR of holograms increased monotonically during dark enhancement, and then it also keeps up a steady value at the low temperature. This process can be attributed to the increment of strong grating in white pixels is obviously higher than that of weak grating in dark pixels, despite rate of the later is higher. In order to demonstrate the decay of hologram quality is related to the diffusion of photoproducts, the time constant τ of decay curve is extracted by nonlinear fitting using Eq. (9). The corresponding diffusion coefficient can be calculated. The temperature dependence of diffusion coefficient is illuminated in Fig. 6. The relationship between diffusion coefficient and temperature for T b Tg can be depicted as [26],
Fig. 7. Lifetime of weak gratings as a function of environmental temperature.
where C1, C2 are the Williams–Landel–Ferry (WLF) coefficients which can be used to described the diffusion process dependent on the temperature. The good agreement between experimental data and theoretical values demonstrates that the decay of stability depended on the diffusion of photoproducts. The characteristic time of decay curves is defined as lifetime of gratings for describing the stability. Fig. 7 represents the lifetime of weak hologram as a function of temperature. The lifetime is remarkably increased as the temperature is reduced. It is indicated that an appropriated temperature can be brought near year lifetime. This curve simultaneously implies that the lifetime of weak hologram is shorter than the lifetime of strong grating which is similar as reference [28].
3.4. Uniform incoherent exposure
ð11Þ
So far, several methods have been presented to improve the stability, such as uniform coherent and incoherent illumination [9,10], baking the sample after exposure [15], and changing the polymerization mechanism [29]. The coherent illumination may bring an amplification of holographic scattering noise and reduction of hologram quality. Therefore final uniform incoherent illumination is an alternative and a simple method for keeping up the long-term stability of holograms, which can be consumed by all the remaining free PQ molecules in the photopolymer. Therefore further holographic recording is prevented. At the saturation of dark enhancement the unreacted PQ molecules are exhausted by uniform exposure, and the exposure time is around 5 h for using up all the free PQ molecules. Then the sample is taken into an oven at 35 °C for thermal treatment. The temporal stability of hologram is measured, as shown in Fig. 8.
Fig. 6. Diffusion coefficient of photoproduct versus temperature. The symbols are the experimental data, and the solid line is fitting curve. The experimental accuracy approached 5%.
Fig. 8. The influence of uniform incoherent exposure on the stability of holograms. The solid and hollow symbols are corresponding to uniform exposure and un-exposure, respectively. The dashes are the corresponding initial time for thermal treatment.
ln ½DðT Þ = C1 = T + C2
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The stability of weak holograms is an important factor for holographic memory. The combination of low temperature and uniform incoherent exposure is the appropriated method for improving the storage stability. This study can improve the understanding of photochemical behaviors and accelerate applicability of PQ-PMMA photopolymers in holographic data storage. Acknowledgements The research has been financially supported by the Fundamental Research Foundation of Commission of Science Technology and Industry for National Defense of China (Grant No. 2320060089).
Fig. 9. The influence of relative humidity on the stability of holograms.
The maximum of refractive index modulation is observed at exposure process. It is implied that the uniform exposure is an efficient method to improving the stability of holograms. Thermal treatment slightly decreases the modulated depth because the photopolymer chains by uniform exposure cannot completely restrain the diffusion of macromolecules of holographic gratings. 3.5. The effect of humidity on hologram qualities Finally the influence of the relative humidity on qualities of holograms is experimentally investigated. We firstly written a hologram in the sample at room temperature, then changed the relative humidity of condition after steady state. The diffraction efficiency and SNR of hologram as a function of relative humidity are shown in Fig. 9. The high humidity can increase the scattered light by vapor and reduce the transmittance of sample, since the qualities of reading holograms would be decreased. However the influence of slight reduction of these values on the stability of holograms is neglectable due to the rigid polymer matrix. 4. Conclusion A detailed experimental study of storage stability in PQ-PMMA photopolymers is presented. The amplification of Bragg detuning was observed during dark diffusion, therefore we must adjust the reading angle for reconstruction. It is demonstrated that the temperature stability of holograms was related to the diffusion of photoproducts.
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